Quantum Sampling Algorithms for Near-Term Devices

Efficient sampling from a classical Gibbs distribution is an important computational problem with applications ranging statistical physics over Monte Carlo and optimization algorithms to machine learning. We introduce family of quantum that provide unbiased samples by preparing state encoding the entire distribution. show this approach leads speedup Markov chain algorithm for several examples including Ising model weighted independent sets two different graphs. Our connects complexity phase transitions, providing physical interpretation speedup. Moreover, it opens door exploring potentially useful on near-term devices as certain graphs can be naturally implemented using Rydberg atom arrays.